Exact bounds on the closeness between the Student and standard normal distributions

Pinelis, Iosif

doi:10.1051/ps/2014014

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Exact bounds on the closeness between the Student and standard normal distributions

Pinelis, Iosif ¹

¹ Department of Mathematical Sciences, Michigan Technological University, Houghton, 49931 Michigan, USA

ESAIM: Probability and Statistics, Tome 19 (2015), pp. 24-27

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Résumé

Upper bounds on the Kolmogorov distance (and, equivalently in this case, on the total variation distance) between the Student distribution with $p$ degrees of freedom ( $S D_{p}$ ) and the standard normal distribution are obtained. These bounds are in a certain sense best possible, and the corresponding relative errors are small even for moderate values of $p$ . The same bounds hold on the closeness between $S D_{p}$ and $S D_{q}$ with $q > p$ . Comparisons with known bounds are made.

Reçu le : 2013-06-13

MR Zbl

DOI : 10.1051/ps/2014014

Classification : 62E17, 60E15, 62E20, 62E15
Keywords: Student’s distribution, standard normal distribution, Kolmogorov distance, total variation distance, probability inequalities

Affiliations des auteurs :

Pinelis, Iosif ¹

¹ Department of Mathematical Sciences, Michigan Technological University, Houghton, 49931 Michigan, USA

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     title = {Exact bounds on the closeness between the {Student} and standard normal distributions},
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     doi = {10.1051/ps/2014014},
     mrnumber = {3374867},
     zbl = {1332.62054},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2014014/}
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Pinelis, Iosif. Exact bounds on the closeness between the Student and standard normal distributions. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 24-27. doi: 10.1051/ps/2014014

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